On 06.05.2011 17:32, Ronan Lamy wrote:
Notice that every element that we ever compute with belongs to some
algebra.
Here's our fundamental disagreement, I think. Objects aren't
intrinsically part of an algebra, they happen to belong to some set over
which some algebraic structure is defined and used.
My point is that without being part of an "algebra" (or whatever we call
it), what does an operation on objects even *mean*, let alone how the
result is represented?
Yes in principle objects are part of sets on which algebraic structures
are (or can be) defined, but for a computer program it is not really
relevant what objects "are", what is relevant is how they are
represented and manipulated. What manipulations are possible is
essentially what I described as "to what algebra does this belong". And
in particular the representation should be chosen in such a way that the
desired manipulations can be done in an efficient fashion.
We are drifting away from assumptions here, but I would argue that in
sympy currently there are about three algebras. They are not being
properly identified as such, and they have no standardised way of
"talking to each other", which makes some things cumbersome. Here they are
o The "calculus" algebra (Add/Mul etc),
o the matrix algebra,
o the polynomial algebras.
Right now the first is meant to encompass everything, but a) it even
doesn't now, b) in the long-term this seems even more unlikely and c) in
any case an all-encompassing algebra can hardly be very efficient for
non-all-encompassing tasks.
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